Self-diffusion data

W. Brown, R. Johnsen, P. Stilbs, B. Lindman. Size and shape of nonionic amphiphile (Ci2Eg) micelles in dilute aqueous solutions as derived from quasielastic and intensity of light scattering, sedimentation and pulsed-field-gradient nuclear magnetic resonance self-diffusion data. J Phys Chem 87 4548-4553, 1983. 

Self-diffusion data [37] derived from NMR PGSE measurements for decane, water, and AOT are illustrated in Fig. 3. The self-diffusion of decane decreases gradually as a decreases from 1.0 to 0.3. The magnitude of decane self-diffusion suggests that the microstructure remains substantially continuous in decane over this composition range. Both water and AOT diffusion initially decrease as a decreases. One can readily see that in this... 

FIG. 3 Self-diffusion coefficients of decane (A), water (B), and AOT ( ) in brine, decane, and AOT microemulsions at 45°C as a function of decane weight fraction, a (relative to decane and brine). Breakpoints in the self-diffusion data for both water and AOT are observed at a = 0.85 and at 0.7. (Reproduced by permission of the American Institute of Physics from Ref. 37.)... 

FIG. 4 Apparent mole fraction (x) water in continuous phase of brine, decane, and AOT microemulsion system derived from the water self-diffusion data of Fig. 3 using the two-state model of Eq. (1). 

FIG. 5 Order parameter for disperse pseudophase water (percolating clusters versus isolated swollen micelles and nonpercolating clusters) derived from self-diffusion data for brine, decane, and AOT microemulsion system of single-phase region illustrated in Fig. 1. The a and arrow denote the onset of percolation in low-frequency conductivity and a breakpoint in water self-diffusion increase. The other arrow (b) indicates where AOT self-diffusion begins to increase. 

Independent self-diffusion measurements [38] of molecularly dispersed water in decane over the 8-50°C interval were used, in conjunction with the self-diffusion data of Fig. 6, to calculate the apparent mole fraction of water in the pseudocontinuous phase from the two-state model of Eq. (1). In these calculations, the micellar diffusion coefficient, D ic, was approximated by the measured self-dilfusion coefficient for AOT below 28°C, and by the linear extrapolation of these AOT data above 28°C. This apparent mole fraction x was then used to graphically derive the anomalous mole fraction x of water in the pseudocontinuous phase. These mole fractions were then used to calculate values for... 

A quantitative analysis of these self-diffusion data according to the two-state model of Eq. (1) to generate the order parameter of Eq. (2) is straightforward. was found to be... 

X 10 cm by measuring molecularly dispersed water in toluene and by correcting for local viscosity differences between toluene and these microemulsions [36]. Values for Dfnic were taken as the observed self-diffusion coefficient for AOT. The apparent mole fraction of water in the continuous toluene pseudophases was then calculated from Eq. (1) and the observed water proton self-diffusion data of Fig. 9. These apparent mole fractions are illustrated in Fig. 10 (top) as a function of... 

While the order parameters derived from the self-diffusion data provide quantitative estimates of the distribution of water among the competing chemical equilibria for the various pseudophase microstructures, the onset of electrical percolation, the onset of water self-diffusion increase, and the onset of surfactant self-diffusion increase provide experimental markers of the continuous transitions discussed here. The formation of irregular bicontinuous microstructures of low mean curvature occurs after the onset of conductivity increase and coincides with the onset of increase in surfactant self-diffusion. This onset of surfactant diffusion increase is not observed in the acrylamide-driven percolation. This combination of conductivity and self-diffusion yields the possibility of mapping pseudophase transitions within isotropic microemulsions domains. 

Fig. 3.28 Melt self-diffusion data for hydrogenated (or deuterated) polybutadiene samples adjusted to 175 °C as a function of molecular weight [82] [83], S [84],H[85],S [86], [87]. (Reprinted with permission from [82]. Copyright 1999 The American Physical Society)...

Figure 14. Solvent (water, methanol) diffusion coefficients of (a) Nafion 117 (EW =1100 g/equiv) and (b) sulfonated poly(arylene ether ketone)s, as a function of the solvent volume fraction. Self-diffusion data (AiaO. T eOi-i) are taken from refs 197, 224, 226, 255—263 and unpublished data from the laboratory of one of the authors) chemical diffusion coefficients (Z>h2o) are calculated from self-diffu-sion coefficients (see text), and permeation diffusion coefficients are determined from permeation coefficients. ...

Table 4.9 Summary of self-diffusion data for divalent cations in aluminosilicate garnets (after Chakraborty and Ganguly, 1991 energy data converted to eV scale, P in kbar). See Chakraborty and Ganguly, 1991, for references.

Figure 9.1 presents self-diffusivity data for DD(dissoc), DD(undissoc), DB, DS, DXL, and DL, for f.c.c. metals on a single Arrhenius plot. With the exception of the surface diffusion data, the data are represented by ideal straight-line Arrhenius plots, which would be realistic if the various activation energies were constants (independent of temperature). However, the data are not sufficiently accurate or extensive to rule out some possible curvature, at least for the grain boundary and dislocation curves, as discussed in Section 9.2.3. 

The fluidity of the solvent is changed because of the structure-breaking effects caused by the presence of macroions. Self-diffusion data on water in the presence of proteins allows one to measure their hydration. This is usually measured in water per gram of anhydrous protein. 

Pulsed-gradient NMR self-diffusion data (22) correlate well with Aeoretical calculations, in which Ae diffusion equation was solved in Ae model geometries by a finite element meAod (Anderson, D. M. Wennerstrdm, H., in preparation) ... 

From the NMR tracer desorption and self-diffusion data (second and third lines of Table I), one obtains the relation Timm > TmlL. In the example given, intercrystalline molecular exchange is limited, therefore, by transport resistances at the surface of the individual crystals. Combined NMR and high-resolution electron microscopy studies 54) suggest that such surface barriers are caused by a layer of reduced permeability rather than by a mere deposit of impenetrable material on the crystal surface, although that must not be the case in general. 

This result is in agreement with recent PFG NMR measurements with oriented ZSM-5 crystals, where the mean self-diffusivity of methane averaged over the straight and sinusoidal channels (i.e., in the x, y plane) has been found to be larger by a factor of 3-5 than the self-diffusivity in the c direction, perpendicular to those 42,43). For the self-diffusion of methane in ZSM-5/silicalite-I, the MD simulations were in very satisfactory agreement with the experimental PFG NMR and QENS self-diffusion data (cf. Refs. 34-38). Furthermore, the degree of a mass transport anisotropy in the MFI framework as predicted by MD simulations (34-38) is compatible with the experimental findings (42,43,49). 

As already discussed, for the partial blocking of ZSM-5 by benzene, the experimental data discussed herein will be compared with two cases of an obstacle distribution (1) in the connecting pore segments or (2) in the channel intersections. Figure 33 compares the experimental results and the computer simulations. For pyridine, the self-diffusion data are in satisfactory agreement with the model for obstacles distributed over the channel intersections. One has to conclude, therefore, that the chemisorbed pyridine molecules and, thus, the Brpnsted acid sites, are localized near or even in the channel intersections. That is to say, all catalytically active centers are accessible for a reactant molecule in a channel intersection. 

L. Endom, H. G. Hertz, B. Thul, and M. D. Zeidler, A Microdynamics Model of Electrolyte Solutions as Derived from Nuclear Magnetic Relaxation and Self-Diffusion Data, Ber. Bunsenges. Phys. Chem. 71,1008-1031 (1967). 

Very recently, a novel Fourier transform NMR method was employed by Lindman, et al. (21) to obtain multicomponent self-diffusion data for some single phase microenulsion systems. Because of the large values obtained for the self-diffusion coefficients of water, hydrocarbon, and alcohol, over a wide range of concentrations, the authors concluded that there are no extended, well-defined structures in these systems. In other words, the Interfaces which separate the hydrophobic from the hydrophilic regions appear to open up and reform at a short time scale. 

Apparent Hydration of the Suspended Microdroplets. The ionic conductivity and water self-diffusion data, divided by the respective values for the bulk liquid, are summarized in Table I, together with the apparent volume fractions p that are calculated from the Maxwell and Hanai mixture theories. The similarity in the ionic conductivity and water self-diffusion data is surprising, in view of the greatly different underlying mechanisms for these phenomena. 

Figs. 1 and 2 depict the result of hierarchical training of a KMC model of benzene in the NaX lattice by simultaneously fitting self-diffusivity data at different loadings 0 (number of benzene molecules per cage) and adsorption isotherms, respectivelyThe optimized... 

Selected Examples. - Pulsed magnetic field gradient (PFG) NMR is today a routine method for the determination of self-diffusion coefficients. However, a remaining goal is the improvement of the precision of the method. The best procedure for the determination of accurate diffusion coefficients by PFG NMR is a calibration with a sample of precisely known D value. Thus Holz et al presented temperature-dependent self-diffusion coefficients of water and six selected molecular liquids. The gained accurate self-diffusion data are suited for an elaborate check of theoretical approaches in the physics of molecular liquids. Price et al examined the translational diffusion... 

Lindman, B. and Stilbs, P. 1982, Characterization of Microemulsion Structure Using Multicomponent Self-diffusion Data, in Surfactants in Solution, Mittal, K. L. and Lindman,... 

For the n-butane-5A system both sorption and ZLC results are in substantial agreement with NMR PFG self diffusivity data. However, for all NaX systems studied the NMR self diffusivities are approximately two orders of magnitude larger than the ZLC values. This discrepancy is difficult to understand. Most of the more obvious explanations can be ruled out on the basis of the experimental evidence. For example, the possible intrusion of extraneous heat and/or mass transfer resistances is excluded by the agreement between the sorption, exchange and ZLC results. For NaX crystals both NMR and ZLC results show that differences in the origin of the sample and the initial dehydration procedure have only a relatively small effect on the diffusivity. (27) The absence of significant surface barriers (for aromatics-NaX) is... 

In recent years there has been a tendency to accept NMR diffusivity data as correct and to assume that where lower diffusivity values are obtained from sorption rate measurements the latter must be in error. The present results suggest that this perspective may not always be correct. Until the origins of the discrepancy are resolved, one must be cautious of accepting NMR self diffusivity data without independent confirmation. 

Figure 5.14 shows high-pressure isobars for the self-diffusion data of the n-alkanes in a plot of log D against log where is the molecular weight. These are the first data obtained with the titanium autoclave described in Section 1.4.2. Such results are commonly described by the Rouse model or by the reptation model, which both predict a linear correlation in this type of plot at constant pressure and temperature this linear correlation is clearly established in Fig. 5.14. Judging from the chain length of the polymethylenes the Rouse model should apply. This model predicts, that D should be proportional to M while the experiments give a D correlation, which is...

Fig. 5.15 High-pressure self-diffusion data for (a) methanol (CH3OH) and (b) water (HjO).

---